Hokkaido Vacation Questions

We are planning to go Hokkaido in end Decemeber. Here is our rough plan:
Day 1: Fly to Hakodate
Day 2: Sight-seeing around Hakodate, stay at onsen
Day 3: Take train to Otaru, stay for 1 night
Day 4: Take train to Noboritbetsu, stay at onsen
Day 5: Take train to Asahikawa, visit Asahiyama Zoo. Overnight at Asahikawa
Day 6: Take train to Biei/Furano, stay in Biei pension
Day 7: Take train to Sapporo
Day 8: Day trip to Kiroro ski resort
Day 9: Shopping day at Sapporo
Day 10: Depart for Tokyo

Questions:
1) Should we buy a 3 or 5 day Hokkaido JR pass?
2) Does the pass cover the transport costs within the city (e.g. Otaru)
3) We would like to rent a car for a day to go around furano and Biei. Is there any car rental pickup available in Furano/Biei? Any maps that we can use?

Appreciate your comments and inputs.

Thanks,
May

That is a lot of intense activity for a holiday, by my relaxed standards.

At the very least you should consider reversing Otaru and Noboribetsu. A look at a Hokkaido map should explain why.

I am curious: what onsen at or near Hakodate are you going to stay at?

Yunokawa Prince

very hard going for sure , a lot of train travel and that is only half of it

Yes, agree that logically we should go Noboribetsu followed by Otaru. But this means that we will miss the Otaru Christmas lightup, so we will probably stick to our plans.

Any advice if we should buy the rail pass?